Long description: fig1c

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A diagram illustrating the hyperbola formed by slicing a cone with a plane that intersects both sides.

Alt text: A diagram illustrating the hyperbola formed by slicing a cone with a plane that intersects both sides.

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  • The image displays a cone with a central dashed line labeled "cone axis".
  • A slanted line, labeled "generator line," is shown slicing through the cone at an angle.
  • The intersection of the plane defined by the "generator line" and the cone's surface forms the shape of a hyperbola.
  • Another illustration shows the hyperbola formed when the slicing plane is parallel to the "cone axis," resulting in a rectangular hyperbola.
  • A final illustration depicts a degenerate case where the plane intersects only along two straight lines.

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